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I hardly use oil at all any more. Generally grease should be used for anything that slides, whereas oil should be used for things that are immersed (pins and such). I pretty much universally use Superlube on all parts, be it gears, compression parts, or the slides on my gbb pistols. It seems to last longer and stay in place better than oil.
The only place I use oil is in the barrel, which I patch it dry to leave a very thin film on the inside of the bore. The theory goes that this helps reduce the buildup of plastic rub-off from the bbs, and requires less work to clean the barrel.

AirsoftGI FMG4-A1: $100 shipped.
This was the early/first versions of the series with the Lonex base. Includes the outer barrel as it is tapered and fits only that receiver. All you need is a rail, inner barrel and maybe a flash hider and you're ready to rock. Upgrades include a full cylinder and APEX Python MOSFET wired to Deans. With the shown 11.1v batteries (info below) and 455mm barrel it shoots 412fps +-2 and 21rps. Can remove the paint on the stock if desired. ZCI 455mm 6.02mm Barrel, R-hopped & lapped: SOLD
Includes the hop up chamber. When paired with the gun above, it was reaching out to 200ft. Please note the price reflects the work/time put into this barrel. It has been lapped 5000 passes down to 0.25 micron as well as had the crown enhanced. A similar package from Clandestine Airsoft would be $125 and would not include the hop up unit.
Lonex Flash Mag $10 shipped or free with the gun
Works fine, holds 360rds. 1 Point Bungie Sling $6 shipped or free with the gun
Does its job.
G&G Crane Stock $25 shipped
Includes buffer tube and mounting hardware ZOP Power 11.1v 5000mah 30C lipo $15 shipped
If you're into redonkulously large batteries, this is for you. Large, works well, wired to Deans. This was included with a gun I bought, so no idea on how many cycles its had.

I lurk. To be honest, Im slowing down with airsoft and getting into firearms. I still play occasionally, but not as much. Same goes with working on guns.
Admin is taking a crack and bringing this place back, and I for one would love to see it back as the active metropolis that it was. I certainly hope with FB cracking down on airsoft sales and groups in general that it drives people back to the forums.

Lets address your 100meter minimum first. While not impossible (longer shots have been made), it is significantly more challenging with AEGs, made even more so by the fact that you have such a long barrel. Barrel length does not dictate range, and can actually hinder it. In your case, for your 100m minimum, it greatly hinders it because you simply don't have enough air volume in the cylinder. You need a higher cylinder air volume to barrel air volume than normal because you will need to push heavy bbs. .43g minimum, but you really need to consider .69g Zr02 bbs to be precise at that range. Those heavy rounds require more air, than say, a .20g or .30g bb. This means you need to actually shorten the barrel. You will need to use a 300mm barrel to get a 3:1 cylinder to barrel volume ratio as a starting point for .45g bbs. If you use .69g, you will need an even shorter barrel. I would recommend getting a bore up cylinder/piston head/cylinder head/air nozzle kit.
Your gun uses a V3 gearbox so you could use a M190 spring. You will need new gears, preferably Seigetek Conceps 20:1 gears. If you purchase a 28TPA motor, you could use their 14:1 gears. You will also need a new motor. Something like an ASG 22000 motor which is 28TPA would be good. Even better if you want to wind you own armature and do something like 32TPA in a neodymium magnet can.
To power all of this you will a powerful 11.1v lipo battery. If you use a M190 spring, 28tpa motor, on 14:1 gears, you will need a battery that can supply at minimum 37amps. I would pick something well above that. You will also need to install a high power MOSFET to handle that electrical load and protect your trigger contacts.
For a barrel, you will want a high quality stainless steel barrel which you should then lap and install the R-hop or ER-hop. The inner barrel will need to be stabilized within the outer barrel.

You keep refering to C like its a magical number for the battery. It's not. The number tells you very little without combining it with the MAH. When you refer to a battey, you need to refer to BOTH C and MAH.
For example:
40C 1000mah battery 40*1.0=40amp discharge capability
20C 2000mah battery 20*2.0=40amp discharge capability
both of those battery will perform very similarly.
10C 5000mah battery 10*5.0=50amp discharge capability
50C 750mah battery 50*0.75=37amp discharge capability
the 10C 5000mah pack is bettery because it can supply more amps if needed.

It's most likely your motor. Change that out and you should be fine. You can always go with a larger battery, but a 39 amp discharge capacity that your firefox has should be sufficient for your gun, provided you change the motor.

SHS motors are rather power hungry, so they heat up quite a bit. You neglect to tell us what the MAH of the batteries are which makes it impossible to tell if they provide sufficient current. Firefox isn't a particularly great brand of lipos.
Also internally, what does your gun have? Knowing all this may help us determine if it is a motor, battery, or build issue. Right now, we don't have a whole lot to go on diagnostically, other that motor.

The Intellect will be the best Nimh out of what you linked. If you can find them, Elite are much better.
For lipo's, these would be better and will fit.
7.4v https://hobbyking.com/en_us/turnigy-nano-tech-1300mah-2s-25-50c-lipo-airsoft-pack.html?___store=en_us
11.1v https://hobbyking.com/en_us/turnigy-nano-tech-1400mah-3s-15-25c-lipo-airsoft-pack-1.html?___store=en_us

Springs settle within the first few thousand rounds. It's a break in period of sort. Hard type springs like PDI and Prometheus will settle less than soft type springs like Systema.
From what you have posted, your guns sounds to be operating properly and within reasonable expectations/parameters.

You will need to run a very light piston for the M110 not to have pre-engagement at 35fps. Ideally, I would recommend a M120 and then short stroke down to your desired fps.
Switch the SHS 14 tooth piston to the SHS 15 tooth piston. It has a little bit better rack support which is very important in a metal tooth piston. You can remove the second tooth when correcting AOE and then swiss cheese it yourself.
You can use Hunterseeker's forumula to determine your ROF with different gear ratios, motors, and batteries. I regularly use it it predict my ROF and it has always been pretty accurate for me. Usually within 2rps or so.
SHS High Torque motors are 16TPA. The problem is that they are hit or miss on quality. Once batch is good, the next heat up like crazy. It's the ACM lottery.
Once you determine your ROF and you know your power output in Joules of the spring, you can solve for how much input power, and thus what battery, you need.

That's a loaded question. Depends on a couple of things, foremost being bb weight, guns power (fps with .20g) and how well you installed the R-hop. The difference between a well done M-nub and the namazu should be minimal if even noticeable.